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CS492(D): Geometric Modeling and Processing

Minhyuk Sung, KAIST, Fall 2021


Teaser1

Time & Location

Time: Mon/Wed 10:30am - 11:45am (KST)
Location: Online via Zoom
(You’ll need a KAIST email address to join.)

Zoom Link

Description

3D content creation is a crucial part of many industries such as graphics, AR/VR, CAD/CAM, and digital fabrication, which tasks typically include designing and creating virtual objects/scenes or reconstructing a real environment. Processing scanned 3D data is also an important problem in many applications as 3D scanning technology is being widely applied, for example, in autonomous driving, robot navigation, and 3D object replication. In this course, we discuss fundamental mathematical methods for geometric 3D modeling and geometric data processing, which can be used (not only in graphics-related fields but) in many other areas in science and engineering. Topics to be covered include the followings:

  • Homogeneous coordinates and geometric transformations
  • Quaternions and their use in modeling 3-d rotations and rigid motions
  • Parametric and implicit representations for curves
  • Algebraic classification of the parametric polynomial curves of low degree
  • Polar forms and the de Casteljau's subdivision algorithm
  • The Bézier representation and the Bernstein basis
  • Splines and continuity constraints
  • B-Splines and the de Boor's algorithm
  • Rational curves
  • Parametric polynomial surfaces and NURBS
  • Subdivision curves and surfaces
  • Triangle meshes for surface representation and reconstruction
  • The quad-edge data structure for manifold subdivision
  • Volumetric representations and conversion algorithms
  • Surface reconstruction from scattered points
  • Scan alignment and shape matching
  • Mesh simplification and fairing
  • Mesh parametrization and other geometry processing algorithms

Prerequisites

The following courses are not required but recommended:

Students are also expected to have good programming skills in C/C++.

Course Staff

Instructor: Minhyuk Sung

  • Email: mhsung@kaist.ac.kr
  • Office hours: By appointment (See #announcements channel in Slack.)

TA: Juil Koo

Course Website: https://mhsung.github.io/kaist-cs492d-fall-2021/
Zoom links, recordings, and slides: KLMS
Homework submission: Gradescope (An invitation will be sent to the registered students by email.)
Quizzes, Q&A, and communication: Discord (An invitation will be sent to the registered students by email.)

Grading

  • Homework (Including Programming Assignments): 50%
  • Midterm Exam: 15%
  • Final Exam: 20%
  • Participation: 15%

Course Logistics

(Last Update: Aug 30, 2021)

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Schedule

(Subject to Change)

Week Date Topic Note
1 Aug 30 Introduction
1 Sep 1 Homogeneous Coordinates; The Projective Plane and 3-Space
2 Sep 6 Oriented Projective Geometry; Euclidean, Affine and Projective Transformations; Matrix Representations
2 Sep 8 Rotations and Quaternions Homework 1 out
3 Sep 13 Shape Modeling: Parametric and Implicit Representations; Classification of Parametric Cubics
3 Sep 15 Polar Forms of Polynomials
4 Sep 20 No Class (Chuseok Holidays)
4 Sep 22 No Class (Chuseok Holidays)
5 Sep 27 Derivatives and Polar Forms; Continuity Constraints
5 Sep 29 Splines and B-Splines Homework 1 due, Homework 2 out
6 Oct 4 Rational Curves
6 Oct 6 Subdivision Curves
7 Oct 11 Tensor-Product and Total Degree Parametric Surfaces
7 Oct 13 Midterm Summary Homework 2 due, Homework 3 out
8 Oct 18 No Class (Midterm)
8 Oct 20 No Class (Midterm)
9 Oct 25 Differential Geometry of Curves
9 Oct 27 Introduction to Shape Acquisition and Geometry Processing 1
10 Nov 1 Introduction to Shape Acquisition and Geometry Processing 2
10 Nov 3 Poisson Surface Reconstruction and Marching Cubes
11 Nov 8 Scan Alignment and Registration; Surface Matching Homework 3 due, Homework 4 out
11 Nov 10 Mesh Simplification
12 Nov 15 No Class (CVPR)
12 Nov 17 No Class (CVPR)
13 Nov 22 Laplace-Beltrami and Other Operators on Meshes. Homework 4 due, Homework 5 out
13 Nov 24 Guest Lecture 1 - Joseph G. Lambourne (Autodesk). Nov 24 (Wed) 5:00 pm KST.
14 Nov 29 Global and local shape descriptors; intrinsic descriptors, heat and wave kernel signatures.
14 Nov 30 Guest Lecture 2 - Tamy Boubekeur (Adobe Research & Ecole Polytechnique). Nov 30 (Tue) 5:00 pm KST.
15 Dec 6 Functional Spaces and Functional Maps, Variations; Map Visualization.
15 Dec 8 Mesh Smoothing, Remeshing, Parametrization, and Course Summary
16 Dec 13 No Class (Final)
16 Dec 15 No Class (Final)

Acknowledgements

Most of the lectures will be based on the materials in the following courses:
Stanford CS348A: Geometric Modeling / Processing
Stanford CS233: Geometric and Topological Data Analysis

  1. Teaser image credits (from left to right):
    Ray et al., Periodic global parameterization, ACM ToG 2006.
    Alliez et al., Recent Advances in Remeshing of Surfaces, Springer 2008.
    https://help.autodesk.com/cloudhelp/2019/ENU/Alias-Tutorials/images/GUID-844B95EE-96B1-4C41-972D-835946754231.png ↩